Found a new problem!
Now I have lots of experience with Austrian polymer pistols, and they work well. However, my M&P has an issue where it spits the brass neatly out to the side and all in one small area.
This can't be right, as my experience with the previously mentioned brand has taught me the brass should fly all over the place, and often bounce off my hat, glasses, face, or - if I'm really lucky - go down the front of my shirt.
The only logical conclusion is that something must be wrong with my M&P.